For a statement involving three variables (say, p, q, r),
the Venn-diagram analysis and the
truth-table analysis are exactly equivalent. Explain this by
showing that the Venn diagram divides the "universe"
into 8 regions, each of which corresponds to one assignment of
0 or 1 to each of p, q, r, i.e. to one row
in the truth table. Extra credit: what happens with 4 variables?